(DGC value =458) Please show steps answers are provided. p of 457 P(or)osS Exerc

Question

(DGC value =458) Please show steps answers are provided. p of 457 P(or)osS Exercise 3.9. (SUSPENSION BRIDGES ARE GOOD ASSETS) A civil engineering company, based on past experience, believes that in 40% of cases bridges collapse due to construction problems, 45% of cases bridges collapse due to design problems, and 15% of cases bridges collapse due to other problems such as earth quakes, heavy vehicular loads etc. Danny is a good designer and claims that there is only log(DGC) %-X. , chance that his design may fail, and also Chris is a good constructor and claims that there is only 0.5 log(DGC) Hs& o Le· chance that his construction may collapse, 15% chances ofcollapsing rern anthe same (osatiktocesis , s*,B))0e0 and assume other 13 Fig. 3.9. Danny Chris Suspension Bridge Assume the construction company bought a design from Danry and later hired Chris as constructor. Unfortunately, the suspension bridge collapsed within the warranty period. (a) What is the conditional probability that the bridge collapsed due to a design problem? .94843 (b )What is the conditional probability that the bridge collapsed due to a construction problem? (o.bl33) ¥/.40S 04 843 Collapsel(?) f(Cp) Colapse) 01337

Explanation / Answer

Here Pr(Danny design fails ) = log (DGC) = log (458) = 2.6609% = 0.0266

Pr(Chrish Manufactur Fails) = 0.5 log(DGC) = 0.5 * log (458) = 1.3304% = 0.0133

(a) Pr(Bridge collapsed due to design problem) = 0.0266 *0.40/ (0.0266 * 0.40 + 0.0133 * 0.45 + 0.15) = 0.0639 = 6.39%

(b) Pr(Bridege collapsed due to manufacturing problem) = 0.0133 * 0.45/ (0.0266 * 0.40 + 0.0133 * 0.45 + 0.15) = 0.0359 = 3.59%

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